Giant coercivity and high magnetic blocking temperatures for N23− radical-bridged dilanthanide complexes upon ligand dissociation

Increasing the operating temperatures of single-molecule magnets—molecules that can retain magnetic polarization in the absence of an applied field—has potential implications toward information storage and computing, and may also inform the development of new bulk magnets. Progress toward these goals relies upon the development of synthetic chemistry enabling enhancement of the thermal barrier to reversal of the magnetic moment, while suppressing alternative relaxation processes. Herein, we show that pairing the axial magnetic anisotropy enforced by tetramethylcyclopentadienyl (CpMe4H) capping ligands with strong magnetic exchange coupling provided by an N2 3− radical bridging ligand results in a series of dilanthanide complexes exhibiting exceptionally large magnetic hysteresis loops that persist to high temperatures. Significantly, reducing the coordination number of the metal centers appears to increase axial magnetic anisotropy, giving rise to larger magnetic relaxation barriers and 100-s magnetic blocking temperatures of up to 20 K, as observed for the complex [K(crypt-222)][(CpMe4H 2Tb)2(μ−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{N}}_2^ \cdot$$\end{document}N2⋅)].


Arrhenius Plot Fitting Details.
The temperature dependence of the magnetic relaxation times recorded on sample of 1-Dy, 1-Tb, 2-Dy, and 2-Tb were analyzed in terms of the contributions of different relaxation processes to the observed relaxation rates. Herein we give the details related to the fitting and interpretation of the results, though the reader is referred to the main text for a broader discussion. The curvature of the plots suggested the occurance of multiple relaxation processes, thus many fits were tried with different incorporated relaxation pathways depending on the sample measurement conditions. The typical magnetic relaxation pathways discussed in the literature, along with their dependence on temperature, are the following: a temperature independent quantum tunneling pathway, Direct relaxation (T or T 2 ), the Raman relaxation process (T n , n = 4, 5, 7, or 9 typically), and the Orbach process (exp(Ueff/kBT)). 5, 6 Note that successful modeling of the Arrhenius plots for 1-Dy, 1-Tb, 2-Dy, and 2-Tb did not require each term, and some were judiciously excluded from the fits depending on the nature of the sample. For example, the data collected on all compounds, at zero dc field were not modeled with the Direct process since the corresponding contribution is nullified in the absence of a dc field. The inclusion of a Raman process did not improve the quality of the fit for 1-Dy and 2-Tb.

Fitting detail for compound 1-Dy
The Arrhenius data for 1-Dy were modeled using equation (1), and the resulting best-fit parameters are given in Supplementary Table 1.
Here, the first term is from the tunneling pathway and the second models an Orbach relaxation pathway. Below 7 K the Arrhenius plot for 1-Dy is nearly temperature independent, which is suggestive of dominant tunneling behavior. Therefore, acceptable fits were obtained by utilizing the first term in equation (1) (see Supplementary Figure 32).

Fitting detail for compound 1-Tb and 2-Dy
The Arrhenius data for 1-Tb and 2-Dy containing data obtained from ac measurements (see Supplementary Figures 37 and 43) were obtained from a linear fit to the Arrhenius expression for the relaxation time: ln(τ) = ln(τ0) + Ueff/kBT.
The Arrhenius data for 1-Tb containing data obtained from ac measurements and dc relaxation experiments were modeled using equation (1), and the resulting best-fit parameters are given in Supplementary Table 1 (see Supplementary Figure 39).
The Arrhenius plot for 2-Dy, composed from relaxation time data obtained from ac measurements and dc relaxation experiments, was modeled using equation (3) and the resulting best-fit parameters are given in Supplementary Table 1.
Here, the first term is from the tunneling pathway, the second is for the Raman process, and the third term models Orbach relaxation pathway (see Supplementary Figure 45).

Fitting detail for compound 2-Tb
The Arrhenius plot for 2-Tb (see Supplementary Figure 49) was constructed from relaxation times obtained from ac measurements where this data modeled using equation (4), and the resulting best-fit parameters are given in Supplementary Table 1. , Here, the two terms model two Orbach relaxation pathways.
The Arrhenius data for 2-Tb (shown as Supplementary Figure 56) where the relaxation times were obtained from ac measurements and dc relaxation measurements were modeled using equation (5), and the resulting best-fit parameters are given in Supplementary Table 1.
Here, the first term is from the tunneling pathway, the second and third term model two Orbach relaxation pathways. Below 14 K, the Arrhenius plot for 2-Tb is nearly temperature independent, which is suggestive of dominant tunneling behavior. Therefore, acceptable fits were obtained by utilizing the first term in equation (5) (see Supplementary Figure 56).

Details of fitting data from dc relaxation experiments for 1-Tb, 2-Dy and 2-Tb
The data from dc relaxation experiments for 1-Tb, 2-Dy and 2-Ln were fitted to a function of the form y = a·exp (−((t/τ) b )) where b is a stretch factor. The fits of the dc relaxation experiments at various temperatures gave the τ (s) and b values listed in Supplementary Tables 2-4. The corresponding dc relaxation experiments are shown in Supplementary Figures 38, 44, 50-55. 4. Details for models of χMT data for 1-Tb, 1-Dy, 2-Tb, and 2-Dy.
Data were modeled using the Hamiltonian: in which corresponds to the magnetic exchange between the radical spin and the multiplets of the lanthanide ions. The operator assigns a uniaxial anisotropy parameter to the lanthanide multiplets. The uniaxial anisotropy of the lanthanide centers was assumed to be large in comparison to the magnitude of magnetic exchange. The value used for the parameter in each model was −150 cm −1 , though variations of this parameter to values as high as −800 cm −1 did not alter the models significantly.
In some cases for later lanthanide-containing systems, including for Tb 3+ and Dy 3+ , when a strongly axial doublet ground state of the Ln 3+ ion is obtained, the magnetic exchange of the total angular momentum of the Ln 3+ ion with an isotropic spin can be assumed to be Ising in nature. 7 The excited state spectrum for a molecule with dominant Ising exchange corresponds to the energies required for different spin flips: where ∆E reflects both the exchange coupling strength and the change in total angular momentum between the ground state (or whichever state from which the spin-flip excitation is occurring) and the spin-flip-generated excited state.
As an example, in 2-Tb, the first excited state corresponds to a flip of one terbium moment, with an energy of (2 6 , or 12 , while the second excited state energy corresponds to a flip of the radical spin, with an energy of (2 12 , or 24 (here the change in angular momenta is between those of the ground and second excited states, rather than between the ground and first excited states).
The Landé g values for the lanthanide multiplets were allowed to vary around their expected gJ values, 1.50 for Tb 3+ and 1.33 for Dy 3+ . Variations from expected gJ values may have a variety of meanings. In the case of 1-Tb, the extremely small variations above 1.50 may potentially be attributed to a small sample mass error, as gJ effectively acts as a scaling parameter in these models. For 2-Tb, the lower than expected g values that provide the best fits may be attributed to a contribution from a coupled higher angular momentum state with a g value below 1.5. 8 Such a contribution is possible even at room temperature due to the strong lanthanide-radical coupling. In contrast, the larger than expected g values that enable the best fits for 1-Dy and 2-Dy are more challenging to rationalize. While mass error is not impossible, the larger deviations from expected gJ for both 1-Dy and 2-Dy suggest a more complex origin. Fortunately, mostly prompts changes in slope of χMT with changing temperature rather than scaling of the χMT product. Since the model tracks changes in slope with decreasing temperature for 1-Dy and 2-Dy reasonably well, the values extracted may be considered reasonable, though certainly not definitive.
A number of models with small variations of gJ and can reasonably reproduce the data for 1-Dy, 1-Tb, 2-Dy, and 2-Tb. As such, multiple models are shown for each χMT versus T data set. For each data set, the model represented by a blue dashed line reflects gJ held constant at its expected value, with allowed to vary to provide the best fit. The model shown as a solid purple line reflects a value, held constant, that generates a spin-flip barrier that best corresponds to the experimental Ueff observed for that complex, with gJ then allowed to vary to provide the best fit. Finally, the model represented by a pink dash-dot line reflects a model in which both and gJ are allowed to vary to generate the best fit to the total data set. Each of these models was generated using the program PHI 9 , with experimental χMT data collected across a temperature range of 20 -300 K, Supplementary Figures 58-59, Supplementary Tables 5 and 6).

Crystallographic data
X-ray diffraction experiments were performed at 100 K on crystals coated with Paratone-N oil and mounted on Kapton or MiTeGen loops. X-ray data were collected at the Small Molecule X-ray Crystallography Facility at the University of California, Berkeley using a Bruker QUAZAR diffractometer equipped with a microfocus sealed X-ray source (Mo Kα radiation; λ = 0.71073 Å) and a Bruker APEX-II detector (for 2-Tb, 4, 3-Dy, Cp Me4H 2Dy(BPh4), Cp Me4H 2Gd(BPh4), Cp Me4H 2TbAllyl, and Cp Me4H 2DyAllyl) or at Beamline 11.3.1 at the Advanced Light Source on a Bruker D8 Diffractometer equipped with a Bruker PHOTON100 CMOS detector using synchrotron radiation (λ = 0.6888 Å for Cp Me4H 2GdAllyl and 1-Dy; λ = 0.7749 Å for 2-Dy, 1-Tb, 1-Gd, 3-Tb, 3-Gd, and Cp Me4H 2Tb(BPh4)). Crystals for 2-Tb, 2-Dy, and 1-Gd were found to be non-merohedral twins based on analysis of their diffraction patterns. For each of these structures, CELL_NOW 10 was used to determine the orientation matrices and raw data for both twin matrices were integrated and corrected for Lorentz and polarization effects using Bruker AXS SAINT 11 software and corrected for absorption using TWINABS. 12 For all other structures, raw data were integrated and corrected for Lorentz and polarization effects using Bruker AXS SAINT 11 software and corrected for absorption using SADABS. 13 Space group assignments were determined by examination of systematic absences, E-statistics, and successive refinement of the structures. All structures were solved by intrinsic phasing using SHELXT. 14 Additional refinement was performed with SHELXL 15 operated within the OLEX2 16 interfaces. Disorder in the structures of 2-Tb, 2-Dy, 1-Tb, 1-Dy, 1-Gd, 3-Tb, 3-Dy, and 3-Gd required the use of displacement parameter restraints in the refinement. The structures for 1-Dy, 1-Gd, 3-Tb, 3-Gd, and Cp Me4H 2GdAllyl gave rise to A and B level alerts from checkCIF. Responses addressing these alerts have been included in the CIFs and can be read in reports generated by checkCIF. Further details are provided in Supplementary Tables 7-9. Variable temperature dc susceptibility data of polycrystalline 1-Dy (orange circles), 1-Tb (blue triangles) and 1-Gd (grey squares) collected under 0.1 T applied dc field. The black line represents a fit to the data for 1-Gd, as discussed in the main text. In a the fit is shown from 2 to 300 K. In b the fit is shown from 75 to 300 K for clarity.  Figure 49. (a, b) Arrhenius plot of the natural log of the relaxation time, τ, versus the inverse temperature obtained from ac measurements, for 1-Tb (green to red circles), 1-Dy (dark blue to red circles), 2-Tb (blue to red circles) and 2-Dy (cyan to red circles). (b) Arrhenius plot for 1-Dy is depicted only for temperatures from 5 to 15 K; the τ below 5 K are omitted for clarity.